Cicadas lay eggs on the new tender twigs I believe. These eggs hatch and the young cicadas drop to the ground, burrow down and feed on the roots with their sucking mouthparts. So I do not think that wrapping a tree would in any way stop them.
Depending upon the type of cicada, their life in the soil is pre-programmed.
If I am not mistaken, the adult cicadas do not have functioning mouth parts. They simply emerge, along a staggered timeline to meet, mate and lay eggs for a new, future brood.